There are two locations useful to you if you're staying in or around the strip; a north and south.
Pricing and services: I haven't been to the further north location, but the south location is in a fairly large building and they carry a huge variety of beer and liquor; pretty much anything you could be looking for will be there, and their pricing is fairly good. You might be able to do a little better further off-strip, but it's not worth the time or money going further as it won't save you that much. I have seen a review (CLICK) that indicated the north location was small.
They do also carry ice, but what they have in the way of coolers is just small party coolers, and they're expensive, so I would not recommend purchasing those at Lee's. If you need to pick up a few larger coolers for an in-suite reception or just a party, I would recommend going to Walmart first (click for a close one), buy the coolers, then hit Lee's and fill them with ice and booze.
Of course, the bathtub makes a decent cooler too (pic courtesy of hstaples4):